Thanks for your reply. I couldn't have been thinking straight earlier since you are perfectly correct about 4n+2, there is even an example for 18 players when you follow the link above!

Here is an updated version of the list with a few more schedules:

8 players10 players - see below

12 players - no balanced schedule exists.

14 players - see below

16 players18 players20 players - no balanced schedule exists

but see here22 players - see below

24 players32 players10 players:

[(H1 W2):(H5 W4)] [(H2 W5):(H4 W1)]

[(H3 W4):(H2 W1)] [(H4 W2):(H1 W3)]

[(H5 W1):(H4 W3)] [(H1 W4):(H3 W5)]

[(H2 W3):(H1 W5)] [(H3 W1):(H5 W2)]

[(H4 W5):(H3 W2)] [(H5 W3):(H2 W4)]

14 players:

[(H6 W3):(H1 W2)] [(H3 W4):(H2 W5)] [(H5 W6):(H4 W1)]

[(H7 W4):(H5 W3)] [(H4 W6):(H3 W2)] [(H2 W7):(H6 W5)]

[(H5 W7):(H3 W6)] [(H7 W1):(H6 W4)] [(H4 W5):(H1 W3)]

[(H4 W2):(H7 W5)] [(H2 W3):(H5 W1)] [(H1 W4):(H3 W7)]

[(H2 W1):(H4 W7)] [(H1 W5):(H7 W6)] [(H6 W2):(H5 W4)]

[(H1 W6):(H2 W4)] [(H6 W7):(H4 W3)] [(H3 W1):(H7 W2)]

[(H3 W5):(H6 W1)] [(H5 W2):(H1 W7)] [(H7 W3):(H2 W6)]

22 players:

[(H01 W10):(H09 W11)] [(H10 W04):(H11 W02)] [(H08 W07):(H03 W05)] [(H05 W09):(H07 W01)] [(H04 W08):(H02 W03)]

[(H02 W07):(H06 W04)] [(H07 W09):(H04 W10)] [(H03 W08):(H05 W11)] [(H11 W06):(H08 W02)] [(H09 W03):(H10 W05)]

[(H08 W05):(H10 W01)] [(H05 W02):(H01 W03)] [(H04 W11):(H09 W06)] [(H06 W10):(H11 W08)] [(H02 W04):(H03 W09)]

[(H03 W11):(H07 W02)] [(H11 W10):(H02 W05)] [(H09 W04):(H06 W01)] [(H01 W07):(H04 W03)] [(H10 W09):(H05 W06)]

[(H11 W09):(H03 W07)] [(H09 W08):(H07 W04)] [(H01 W06):(H02 W10)] [(H10 W03):(H06 W11)] [(H08 W01):(H04 W02)]

[(H07 W03):(H02 W06)] [(H03 W01):(H06 W08)] [(H11 W05):(H04 W09)] [(H09 W02):(H05 W07)] [(H01 W11):(H08 W04)]

[(H10 W08):(H01 W09)] [(H08 W06):(H09 W07)] [(H05 W03):(H11 W04)] [(H04 W01):(H03 W10)] [(H06 W05):(H07 W11)]

[(H09 W01):(H11 W03)] [(H01 W05):(H03 W06)] [(H10 W02):(H07 W08)] [(H08 W11):(H02 W09)] [(H05 W10):(H06 W07)]

[(H06 W02):(H04 W05)] [(H02 W11):(H05 W01)] [(H07 W10):(H08 W03)] [(H03 W04):(H10 W06)] [(H11 W07):(H01 W08)]

[(H05 W04):(H08 W10)] [(H04 W07):(H10 W11)] [(H06 W09):(H01 W02)] [(H02 W08):(H09 W05)] [(H07 W06):(H11 W01)]

[(H04 W06):(H05 W08)] [(H06 W03):(H08 W09)] [(H02 W01):(H10 W07)] [(H07 W05):(H01 W04)] [(H03 W02):(H09 W10)]